Elliptic curve isogeny class with LMFDB label 53.a (Cremona label 53a)

• Label: 53.a
• Number of curves: $1$
• Conductor: $53$
• CM: no
• Rank: $1$

Rank

The elliptic curve 53.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53.a do not have complex multiplication.

Modular form 53.2.a.a

Elliptic curves in class 53.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53.a1	53a1	\([1, -1, 1, 0, 0]\)	\(3375/53\)	\(-53\)	\([]\)	\(2\)	\(-0.98855\)	\(\Gamma_0(N)\)-optimal